Hi all,

I’m working on a Gaussian Process model, using it to estimate interdependence between observations (military alliances). The challenge is that while most GP applications I can find use the interdependence as a control or examine the impact of various predictors, I want to examine how changing the outcome value in one unit impacts the outcome in all other units.

So far, the best I could come up with is to take some observed data, changing the outcome in one unit, and leaving the rest. Unfortunately, the posterior predictions are exactly the same, despite non-zero correlations between some units in the GP.

Here’s the code- can send data if anyone is interested in tinkering with it directly.

```
# load packages
library(brms)
library(tidyverse)
# run model
cred_mod_noar <- ordbetareg(irt_median ~ bilat + mean_kappa_atop +
mean_v2x_polyarchy + us_solsch + log_troops +
gp(mean_lat, mean_long,
k = 20,
cov = "exp_quad",
c = 5/4,
scale = TRUE,
gr = FALSE, iso = TRUE),
cores = 4,
refresh = 500,
backend = "cmdstanr",
control = list(adapt_delta = .99,
max_treedepth = 20),
data = cred_data)
summary(cred_mod_noar)
# calculate impact of fall in Phillipine credibility (Duterte)
cred_data <- cred_data %>%
group_by(cred_recip) %>%
mutate(
change_cred = irt_median - lag(irt_median)
) %>%
ungroup()
max_fall <- min(cred_data$change_cred, na.rm = TRUE)
max_fall
filter(cred_data, change_cred == max_fall)
cred_orig <- filter(cred_data, year == 2015)
# predictions with original data
pred_orig <- posterior_epred(cred_mod_noar, newdata = cred_orig)
# new predictions
cred_shift <- cred_orig
cred_shift$irt_median[cred_shift$cred_recip == "Philippines"] <- cred_shift$irt_median[cred_shift$cred_recip == "Philippines"] + max_fall
pred_change <- posterior_epred(cred_mod_noar, newdata = cred_shift)
# Calculate the change in predictions
effect_change <- pred_change - pred_orig
summary(effect_change)
```

Should I be working with the covariance matrix for the GP more directly? Clarification if I have misunderstood the nature of how GPs model interdependence is very welcome also.

- brms Version: 2.21.0

Thanks for your time and help!